Model-theoretic Tameness in finite extensions of groups
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918501136990208 |
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| author | Halevi, Yatir Shelah, Saharon |
| author_facet | Halevi, Yatir Shelah, Saharon |
| contents | It is shown that finite-index extensions and finite-index subgroups of $ω$-stable groups can be model-theoretically wild. More precisely, there exists an $ω$-stable group $G$ such that any given countable first-order structure in a finite language is interpretable both in some finite-index extension of $G$ and in some finite-index subgroup of $G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_14390 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Model-theoretic Tameness in finite extensions of groups Halevi, Yatir Shelah, Saharon Logic Group Theory It is shown that finite-index extensions and finite-index subgroups of $ω$-stable groups can be model-theoretically wild. More precisely, there exists an $ω$-stable group $G$ such that any given countable first-order structure in a finite language is interpretable both in some finite-index extension of $G$ and in some finite-index subgroup of $G$. |
| title | Model-theoretic Tameness in finite extensions of groups |
| topic | Logic Group Theory |
| url | https://arxiv.org/abs/2605.14390 |